Chapter 22, Problem 59GP

Neutral hydrogen can be modeled as a positive point charge + 1.6 × 10⁻¹⁹ C surrounded by a distribution of negative charge with volume density given by ${\rho }_{\text{E}}(r)=-A{e}^{-2r/a_0}$ where a₀ = 0.53 × 10⁻¹⁰ m is called the Bohr radius, A is a constant such that the total amount of negative charge is −1.6 × 10⁻⁹ C, and $e=2.718\cdots$ is the base of the natural log. (a) What is the net charge inside a sphere of radius a₀? (b) What is the strength of the electric field at a distance a₀ from the nucleus? [Hint: Do not confuse the exponential number e with the elementary charge e which uses the same symbol but has a completely different meaning and value (e = 1.6 × 10⁻¹⁹C).]